Question

A person needs to locate a staircase to be able to climb to the second floor of a house if the angle of inclination of the staircase is 30 degrees and the height from the first to the second floor of the house is 2.75 meters. What is the measurement of the distance where you should put the base of the ladder?

Answer 1

To reach a height of 2.75 meters with a ladder inclined at 30 degrees, the base of the ladder must be placed 5.5 meters from the house, as calculated using sine(30 degrees) = opposite/hypotenuse.

Step-by-step explanation:

To calculate the distance where you should place the base of the ladder to reach a height of 2.75 meters with an inclination angle of 30 degrees, we can use the trigonometric function of a right triangle.

This problem involves the sine function, where sine is defined as the ratio of the opposite side (height of the triangle) over the hypotenuse (the length of the staircase).

Here, the opposite side is the height of the second floor, 2.75 meters, and we are solving for the hypotenuse which is the distance from the base of the house to the base of the ladder.

The sine of 30 degrees is equal to 1/2 or 0.5.

Therefore, we can set up the equation sine(30 degrees) = 2.75 meters/hypotenuse.

Solving for the hypotenuse, we find that hypotenuse = 2.75 meters/sine (30 degrees) = 2.75 meters / 0.5 = 5.5 meters.

Thus, the base of the ladder needs to be placed 5.5 meters from the house.